Syllabus
In the course the languages of the following fundamental mathematical theories: elementary arithmetic, synthetic geometry, algebra, analytic geometry differential and integral calculus, fractal geometry, predicate logic, set theory will be analyzed from the point of view of six basic linguistic parameters: logical power, expressive power, methodological power, integrative power explanatory power, and metaphorical power.
Annotation
Introduction to the study of the history of mathematics. The first historical mathematical texts.
Egypt - notation of numbers, arithmetic operations, some computational problems, geometry: areas of planar figures. Mesopotamia - cuneiform symbols of numbers, approximate methods of arithmetic calculations, tabulation of arithmetic operations, quadratic equations.
Mathematics in Ancient Greece. Pythagorean teachings of even and odd.
Irrationalities and Eudox's theory of quantities. Classical geometric problems (trisection of the angle, quadrature of a circle and doubling of a cube).
The axiomatic system of Euclids Elements. Proof of Pythagorean Theorem.
Criticism of the axiom about parallel lines. Zenon's aporia.
Eudox's exhaustive method. Archimedes quadrature of the parabola segment.
Mathematics of China, India, their character and influence on Arabic written mathematical texts. European familiarization with the results of oriental mathematics.
The first independent results of European mathematics.